Term vereinfachen: (5a + b)(a - 2b)(a + 3b) - a(a - 4b)(5a + b) + 6b^3

Question

(5a + b)(a - 2b)(a + 3b) - a(a - 4b)(5a + b) + 6b^3

Answer 1

(5a + b)(a - 2b)(a + 3b) - a(a - 4b)(5a + b) + 6b^3
= (5a^2 - 9ab - 2b^2)(a + 3b) - a(5a^2 - 19ab - 4b^2) + 6b^3
= (- 6b^3 - 29ab^2 + 6a^2·b + 5a^3) - (5a^3 - 19a^2·b - 4ab^2) + 6b^3
= - 6b^3 - 29ab^2 + 6a^2·b + 5a^3 - 5a^3 + 19a^2·b + 4ab^2 + 6b^3
= 25a^2·b - 25a·b^2
= 25ab(a - b)

Answer 2

Hi,

(5a+b)(a-2b)(a+3b)-a(a-4b)(5a+b)+6b³

 

=(5a^2-10ab+ab-2b^2)(a+3b)-(a^2-4ab)(5a+b)+6b^3

=5a^3-10a^{2}b+a^{2}b-2ab^2+15a^{2}b-30ab^2+3ab^2-6b^3-(5a^3+a^{2}b-20a^{2}b-4ab^2)+6b^3

=5a^3-10a^{2}b+a^{2}b-2ab^2+15a^{2}b-30ab^2+3ab^2-6b^3-5a^3-a^{2}b+20a^{2}b+4ab^2+6b^3

=25a²b-25ab^2

 

Grüße

Answer 3

Die Klammern miteinander multiplizieren

(5a²-10ab+ab-2b²)  (a+3b)   -a   ( 5a²+ab-20ab-4b²)   +6b³    | in der Klammer zusammenfassen

(5a²-9ab-2b²) ( a+3b) -a (5a²-19ab-4b²) +6b³                           | nochmal multiplizieren

5a³+15a²b-9a²b-27ab²-2ab²-6b³ -5a³+19a²b +4ab² +6b³          | nun wieder zusammenfassen

25a²b -25ab²                                                                          | Distributivgesetz anwenden

25ab ( a-b)